Math help pls?

The distance (d) to the visible horizon varies directly with the square root of the height (h) of the observer above sea level. An observer 1.8m tall can see 4.8km out to sea when standing on the shoreline.
a) how far could the person see if they climbed a 4m tower?
b)if the top of a 10m mast on a yacht is just... show more The distance (d) to the visible horizon varies directly with the square root of the height (h) of the observer above sea level. An observer 1.8m tall can see 4.8km out to sea when standing on the shoreline.

a) how far could the person see if they climbed a 4m tower?

b)if the top of a 10m mast on a yacht is just visible to the observer in the tower, how far out to sea is the yacht.

I've tried to find k using 4800=k(sqrt(1.8)) But the value seems unrealistic and doesn't provide the correct answer where am i going wrong? answer to a is 8.616km and answer to b is 19.93km

So, the top of the mast is equivalent to being 10 m higher (as the top of the mast becomes reference instead of ground/horizon)
d = 3,577.71 (15.8)^0.5
d = 14,221 m = 14.221 km

You seem to have been on the same right track as me.
Not sure how they are getting the value for b).
Back calc'ing it, gives an h ~ 31 m; which I do not get.

Edit: Mike G clued me in. Find the distance for h = 5.8 m then add the distance for h = 10 m. Seeing the top of the mast is equivalent to eye level being at 10 m. So, add the distance as though you were standing at the mast.